
In the recent years, some authors have generalized the linear canonical transform to quaternion-valued signals, known as the quaternionic linear
canonical transform (QLCT). The QLCT was firstly studied in [1]} including prolate spheroidal wave signals and uncertainty principles [2]}. Some useful properties of the QLCT such as linearity, reconstruction formula, continuity, boundedness, positivity inversion formula and the uncertainty principle were established in [3]}, [4]}, [5]}, [6]}. An application of the QLCT to study of generalized swept-frequency filters was introduced in [7]}. Because of the non-commutative property of multiplication of quaternions, there are mainly three various types of 2D quaternion linear canonical transform (QLCTs): two-sided QLCTs, left-sided QLCTs and right-sided QLCTs (refer to [2]}). Based on the (two-sided) QLCT [1]}, the quaternion windowed linear canonical transform of 2D quaternionic signals has been introduced by Wen-Biao Gao and Bing-Zhao Li in [10]}. It can reveal the local QLCT-frequency contents and enjoys high concentrations and eliminates the cross term, but it has limitation of having fixed window localization.
